Affine Toda field theory on a half line

TL;DR

This paper investigates the integrability of affine Toda field theory on a half-line, revealing strict boundary conditions necessary for preserving integrability and exploring classical and quantum boundary phenomena.

Contribution

It demonstrates that boundary conditions preserving integrability in affine Toda models are highly constrained, with no free parameters for the $a_n$ series, and links classical boundary states to quantum reflection factors.

Findings

Boundary conditions are strongly constrained for integrability.

No free parameters exist in boundary conditions for $a_n$ models.

Classical boundary bound states relate to quantum reflection factors.

Abstract

The question of the integrability of real-coupling affine toda field theory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained. In particular, for the $a_n\ (n>1)$ series of models there can be no free parameters introduced by the boundary condition; indeed the only remaining freedom (apart from choosing the simple condition $\partial_1\phi =0$), resides in a choice of signs. For a special case of the boundary condition, it is argued that the classical boundary bound state spectrum is closely related to a consistent set of reflection factors in the quantum field theory.